Following from the finiteness of speed, the average length of the steps must
be finite. I consequently abandon the notion of diffusivity in
this work. By doing so, the
random walk is characterized by the mean free path \(\ell \) .
Massless particles experiencing an equivalent of Brownian motion
compatible with the principles of special relativity therefore
perform a continuous time persistent random walk (CTPRW) as
originally defined by Masoliver, Lindenberg and Weiss [1]}.
The Fokker-Planck equation associated to the CTPRW process is
Chandraskhar's radiative transfer equation [2]},
that is discussed here in one and two dimensions.
Following the work of Dudley [3]},
the CTPRW in this Letter are not defined as stochastic processes
in physical space,
like Brownian
motion, but as stochastic processes in phase space.
